Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory

TL;DR

This paper explores the phase structure and critical phenomena in N=1 super Yang-Mills theory with an adjoint Higgs, revealing new critical points, phase transitions, and a double scaling limit leading to a non-critical string theory.

Contribution

It introduces a novel double scaling limit in N=1 super Yang-Mills, connecting gauge theory critical points to non-critical string theories and analyzing phase transitions with fractional Nc scaling.

Findings

Identification of critical points with massless states and tensionless domain walls

Description of phase transitions between different gauge symmetry breaking patterns

Establishment of a double scaling limit yielding exact brane tensions

Abstract

We study the physics of N=1 super Yang-Mills theory with gauge group U(Nc) and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large Nc expansion is singular near the critical points, with domain walls tensions scaling as a fractional power of Nc. We argue that the critical points are four dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting N=1, four dimensional non-critical string theory. D-brane states can be deformed continuously into closed string solitonic states and vice-versa along paths that go over regions where the string coupling is strong.